Faster blur effect in Blender VSE
Since I figured out the answer, I'll answer my own question.

Blender's Video Sequence Editor is an awesome tool; however, it lacks some functionality like some effects the Compositor has.

For example, there is no Fast Gaussian Blur which is a lot faster than the normal Gaussian Blur with a minor margin of error (see this page for a comparison; it's not exactly the Blender's implementation, but it's pretty close). Furthermore, as far as my preferences go, I actually prefer the look of the Fast Gaussian to the normal Gaussian Blur.

So, since there's no direct way of using the compositing feature for the video strips, the question is, are there any workarounds?

Fortunately, I was able to find a working add-on for that, it's called Edit Strip With Compositor.

Note: There's another add-on mentioned in this thread called VSE to Compositor, but it doesn't work for Blender 2.76b.

So, let's get to it.

In order to install and enable it, follow these steps:


Firstly, download the latest version (it's the version 0.14 for Nov
20, 2015).
Next we need to extract the Python script from the archive.
Now, you can either install the script from the User Preferences or if you want to make it system-wide, you can copy it to the Blender's add-ons folder (in my system it's /usr/share/blender/2.76/scripts/addons). Note that this might require some administrative privileges.
Then you need to go to the User Preferences in Blender and activate the add-on.
If you want to enable it by default (on Blender's startup), don't forget to click the Save User Settings button.


After enabling it, you can start using the compositing functionality for the VSE. Here's a demo of it; however, he uses the other add-on mentioned above in the note, but they're not that different.

To apply the effects from the Compositor to the VSE strip, you need to follow these steps:


Select a video strip first (yes, unfortunately, you cannot apply the effects to the effects strips itself, but you can apply other effects on top of it).
Press N on your keyboard to open the Properties panel.
Scroll down in the Properties panel until you see the Edit strip with Compositor section.
Click the Set master scene button.
Check the Show options checkbox.
In the Compositing, choose the Compositing option from the drop-down list.
In the Editing Screen, choose the Video Editing option.
Optionally, you can enable the Add Viewer option.
Click the Create Comp from strip button on top of the section.
Click the Edit Composition button.
Now, this should look familiar. It should get you to the Blender's Compositor. Let's add the Blur effect. Open the Add menu by pressing Shift+A and select Filter → Blur from there.
Drag the Blur node over the connection path and once it becomes white, make a single click.
From the drop-down menu, select Fast Gaussian instead of Gaussian and choose your X and Y values for the blur size.


It should look something like this (except for the Backdrop which I have disabled):



Switch back to the Video Editor layout and voilà! You can notice that the blur effect is much more responsive now.
In order to animate the effects, you need to switch back to the Compositor and utilize the keyframing from there.


Related questions:


Can I add the output of the VSE as input to the node diagram? — Blender Stack Exchange
Blur video track in Video Editor? — Blender Stack Exchange